You can directly connect to the Switch over a wifi network it creates. You can select up to 10 photos to share at a time. It'll create a one-time-use wifi network (the connection details are different every time) and generate a QR code so you can connect to it. After your phone is connected, it'll generate another QR code that'll direct you to a webpage (a local IP address, specifically) where you can browse and download the photos from.
Make sure to turn off data on your phone while you're trying to do this. Some phones use data as a fallback if the wifi network they're connected to isn't connected to the internet.